The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein “two-point step size” strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the Barzilai-Borwein strategy yields a method with an R-linear rate of convergence when it is employed to minimize a strongly convex quadratic. … Read more
A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems and Bounded Knapsack … Read more
We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader’s problem. Both bounding problems are equivalent to explicit mixed-integer linear programs … Read more
In this work, we propose a predictor-corrector interior point method for linear programming in a primal-dual context, where the next iterate is chosen by the minimization of a polynomial merit function of three variables: the first is the steplength, the second defines the central path and the third models the weight of a corrector direction. … Read more
We study same-day delivery systems by formulating the Dynamic Dispatch Waves Problem (DDWP), which models a distribution center where geographically located delivery orders realize dynamically throughout the day. At each decision epoch (wave), the system’s operator chooses whether or not to dispatch a vehicle route loaded with orders ready for service, to minimize vehicle travel … Read more
Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward feasible points that have lower (not necessarily minimal) values of the objective function than points that would have been reached by the same … Read more
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear … Read more
We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. In particular, the proposed method enables … Read more
We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also show that Block BFGS is globally convergent to a stationary point when applied to non-convex functions with bounded Hessian, and … Read more
We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satis ed probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. … Read more